I was under the impression that Ashkenazi and Sephardic Jews derived from that population in Rome? Did the Ashkenazi come directly from Palestine to the Rhine valley?

I think you are right.

This is a good if somewhat technical book on this: Legacy: A Genetic History of the Jewish People https://www.amazon.com/gp/product/B008MWL9HG/

Quote:

The Jewish community of Rome is among the oldest, historically continuous Jewish populations. Jews resided in Rome during the Roman Empire and were brought to Rome by the Emperor Titus, following the suppression of the Bar Kochba rebellion and the destruction of the Jewish Temple in Jerusalem in 70 C.E. Spanish Jews came to Rome during the Inquisition and, paradoxically, were shielded from the hostility of their Roman Jewish neighbors by the Pope. Over time, the Sephardic and Roman Jewish communities co-mingled. Jews from Rome crossed the Alps to populate the Rhine Valley and establish Ashkenazim. So Rome has been a crossroads for Jews from different communities during their histories.

[...] Many members of the Roman Jewish community were fond of telling us that they were neither Sephardic nor Ashkenazi. Our study from that time demonstrated that the Roman Jews had a low frequency of disease mutations that were found in both Ashkenazi and Sephardic populations, supporting the notion that they may have been a progenitor population for Ashkenazi Jews and that they had Sephardic roots.

Some Ashkenazim trace ancestry to Lucca (according to various accounts, they were invited to what's today Germany by Charlemagne). However, there are ancient Jewish tombstones discovered in Cologne for instance, which predate that by hundreds of years. Either way, Sephardim had a separate migration path.